Dissipative instability in partially ionised prominence plasmas

We investigate the nature of dissipative instability at the boundary (seen here as tangential discontinuity) between the viscous corona and the partially ionised prominence plasma in the incompressible limit. The importance of the partial ionisation is investigated in terms of the ionisation fraction. Matching the solutions for the transversal component of the velocity and total pressure at the interface between the prominence and coronal plasmas, we derive a dispersion relation whose imaginary part describes the evolution of the instability. Results are obtained in the limit of weak dissipation. Using simple analytical methods, we show that dissipative instabilities appear for flow speeds that are lower than the Kelvin-Helmholtz instability threshold. While viscosity tends to destabilise the plasma, the effect of partial ionisation (through the Cowling resistivity) will act towards stabilising the interface. For ionisation degrees closer to a neutral gas the interface will be unstable for larger values of equilibrium flow. The same principle is assumed when studying the appearance of instability at the interface between prominences and dark plumes. The unstable mode appearing in this case has a very small growth rate and dissipative instability cannot explain the appearance of flows in plumes. The present study improves our understanding of the complexity of dynamical processes at the interface of solar prominences and solar corona, and the role partial ionisation can have on the stability of the plasma. Our results clearly show that the problem of partial ionisation introduces new aspects of plasma stability with consequences on the evolution of solar prominences.Comment: 8 pages, 2 figure

Mean shear flows generated by nonlinear resonant Alfven waves

In the context of resonant absorption, nonlinearity has two different manifestations. The first is the reduction in amplitude of perturbations around the resonant point (wave energy absorption). The second is the generation of mean shear flows outside the dissipative layer surrounding the resonant point. Ruderman et al. [Phys. Plasmas 4, 75 (1997)] studied both these effects at the slow resonance in isotropic plasmas. Clack et al. [Astron. Astrophys. 494}, 317 (2009)] investigated nonlinearity at the Alfven resonance, however, they did not include the generation of mean shear flow. In this present paper, we investigate the mean shear flow, analytically, and study its properties. We find that the flow generated is parallel to the magnetic surfaces and has a characteristic velocity proportional to $\epsilon^{1/2}$, where $\epsilon$ is the dimensionless amplitude of perturbations far away from the resonance. This is, qualitatively, similar to the flow generated at the slow resonance. The jumps in the derivatives of the parallel and perpendicular components of mean shear flow across the dissipative layer are derived. We estimate the generated mean shear flow to be of the order of $10{\rm kms}^{-1}$ in both the solar upper chromosphere and solar corona, however, this value strongly depends on the choice of boundary conditions. It is proposed that the generated mean shear flow can produce a Kelvin--Helmholtz instability at the dissipative layer which can create turbulent motions. This instability would be an additional effect, as a Kelvin--Helmholtz instability may already exist due to the velocity field of the resonant Alfven waves. This flow can also be superimposed onto existing large scale motions in the solar upper atmosphere.Comment: 11 page

Nonlinear resonant absorption of fast magnetoacoustic waves in strongly anisotropic and dispersive plasmas

The nonlinear theory of driven magnetohydrodynamics (MHD) waves in strongly anisotropic and dispersive plasmas, developed for slow resonance by Clack and Ballai [Phys. Plasmas 15, 2310 (2008)] and Alfvén resonance by Clack et al. [Astron. Astrophys. 494, 317 (2009)] , is used to study the weakly nonlinear interaction of fast magnetoacoustic (FMA) waves in a one-dimensional planar plasma. The magnetic configuration consists of an inhomogeneous magnetic slab sandwiched between two regions of semi-infinite homogeneous magnetic plasmas. Laterally driven FMA waves penetrate the inhomogeneous slab interacting with the localized slow or Alfvén dissipative layer and are partly reflected, dissipated, and transmitted by this region. The nonlinearity parameter defined by Clack and Ballai (2008) is assumed to be small and a regular perturbation method is used to obtain analytical solutions in the slow dissipative layer. The effect of dispersion in the slow dissipative layer is to further decrease the coefficient of energy absorption, compared to its standard weakly nonlinear counterpart, and the generation of higher harmonics in the outgoing wave in addition to the fundamental one. The absorption of external drivers at the Alfvén resonance is described within the linear MHD with great accuracy

New approach for analysing dynamical processes on the surface of photospheric vortex tubes

The majority of studies on multi-scale vortex motions employ a two-dimensional geometry by using a variety of observational and numerical data. This approach limits the understanding the nature of physical processes responsible for vortex dynamics. Here we develop a new methodology to extract essential information from the boundary surface of vortex tubes. 3D high-resolution magnetoconvection MURaM numerical data has been used to analyse photospheric intergranular velocity vortices. The Lagrangian Averaged Vorticity Deviation (LAVD) technique was applied to define the centers of vortex structures and their boundary surfaces based on the advection of fluid elements. These surfaces were mapped onto a constructed envelope grid that allows the study of the key plasma parameters as functions of space and time. Quantities that help in understanding the dynamics of the plasma, e.g. Lorentz force, pressure force, plasma-$\beta$ were also determined. Our results suggest that, while density and pressure have a rather global behaviour, the other physical quantities undergo local changes, with their magnitude and orientation changing in space and time. At the surface, the mixing in the horizontal direction is not efficient, leading to appearance of localized regions with higher/colder temperatures. In addition, the analysis of the MHD Poynting flux confirms that the majority of the energy is directed in the horizontal direction. Our findings also indicate that the pressure and magnetic forces that drive the dynamics of the plasma on vortex surfaces are unbalanced and therefore the vortices do not rotate as a rigid body

Nonlinear theory of resonant slow waves in anisotropic and dispersive plasmas

The solar corona is a typical example of a plasma with strongly anisotropic transport processes. The main dissipative mechanisms in the solar corona acting on slow magnetoacoustic waves are the anisotropic thermal conductivity and viscosity [Ballai et al., Phys. Plasmas 5, 252 (1998)] developed the nonlinear theory of driven slow resonant waves in such a regime. In the present paper the nonlinear behavior of driven magnetohydrodynamic waves in the slow dissipative layer in plasmas with strongly anisotropic viscosity and thermal conductivity is expanded by considering dispersive effects due to Hall currents. The nonlinear governing equation describing the dynamics of nonlinear resonant slow waves is supplemented by a term which describes nonlinear dispersion and is of the same order of magnitude as nonlinearity and dissipation. The connection formulas are found to be similar to their nondispersive counterparts

Nonlinear effects in resonant layers in solar and space plasmas

The present paper reviews recent advances in the theory of nonlinear driven magnetohydrodynamic (MHD) waves in slow and Alfven resonant layers. Simple estimations show that in the vicinity of resonant positions the amplitude of variables can grow over the threshold where linear descriptions are valid. Using the method of matched asymptotic expansions, governing equations of dynamics inside the dissipative layer and jump conditions across the dissipative layers are derived. These relations are essential when studying the efficiency of resonant absorption. Nonlinearity in dissipative layers can generate new effects, such as mean flows, which can have serious implications on the stability and efficiency of the resonance